An optical-grade surfacing tool includes: a rigid holder (60); an elastically compressible interface (12) secured to the rigid holder (60); and a flexible pad (13) that can be applied against a surface to be machined (71) and secured to the interface (12) opposite the rigid holder (60). The pad (13) is carried by an elastically extensible membrane (14) including: a central plate (15); and a plurality of straps (18) each radially protruding from the periphery of the plate (15) and each having a distal portion engaged with a fastening element (38), each strap (18) rotating about the side surface (28) of the interface (12) and extending up to the fastening element, each strap (18) being taut.